Quantas do not need mass property
We believe that the ultimate sub quanta because being the ultimate, it is not made of something else and cannot have the property called mass. We have to make sure that the concept of mass is well understood. Mass is not energy but a concept used to described how the interaction between matter and matter or between matter and non-matter. If the interaction causes matter to change its velocity, then we have the concept of energy since energy is a measure of that change.
If we accept that all matter is made of a multitude of last sub quanta that are organised in a certain way, then it is easier to understand how these quanta can change the velocity of matter even without having any mass.
When many quantas interact with matter, they become part of that matter. The system called matter is then reorganised and contains these quantas. It is possible for that matter to emit quantas and usually the average amount of quantas in that matter remains almost the same. If more quantas are arriving from one side of matter, then matter is reorganised a bit farther as if it was pushed. There is no real pushing force but only matter reorganised at a different position in space. An observer will think that a force has acted on matter.